Show that the system of equations
` 4 x + 6y = 7, 12 x + 18 y = 21 `
has infinitely many solutions.

Explanation

The given system of equations is
` 4x + 6y - 7 = 0 , 12 x + 18 y - 21 = 0 `
These equations are of the form
` a_1 x + b_ 1 y + c_ 1 =0 and a_ 2 x + b_ 2 y + c _ 2 = 0 `
where ` a_1= 4 , b_ 1 = 6, c_ 1 = - 7 and a_ 2 = 12, b_ 2 = 18, c_ 2 = -21 `
` therefore (a_ 1 )/( a_ 2) = ( 4)/( 12) = (1 )/(3), (b_ 1 ) /(b _ 2 ) = ( 6) /( 18 ) = (1)/(3) and (c_ 1 ) /( c_ 2) = (( - 7) /( - 21 )) = (1)/(3)`.
Thus, ` (a_ 1 ) /( a_ 2 ) = (b_ 1) /(b _ 2) = (c _ 1) /(c _ 2)`
Hence, the given system of equations has infinitely many solutions.